Title: Random surface covariance estimation by shifted partial tracing
Authors: Victor Panaretos - EPFL (Switzerland) [presenting]
Abstract: The problem of covariance estimation is considered for replicated surface-valued processes from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the covariance, even though the assumption may fail in practice. We consider a setting where the covariance structure may fail to be separable locally either due to noise contamination or due to the presence of a non-separable short-range dependent signal component. That is, the covariance is an additive perturbation of a separable component by a non-separable but banded component. We introduce nonparametric estimators hinging on the novel concept of shifted partial tracing, enabling computationally efficient estimation of the model under dense observation. Due to the denoising properties of shifted partial tracing, the methods are shown to yield consistent estimators even under noisy discrete observation, without the need for smoothing. Further to convergence rates and limit theorems, we show that the implementation of our estimators, including for the purpose of prediction, comes at no computational overhead relative to a separable model.